A proof of Corollaries REF , REF  and
REF  can be found in Appendices ,
 and , respectively. We are now
ready to prove Theorem REF . Note that the special
case with \(\mathbf {M}_1=\mathbf {M}_2=0\)  was proved in Corollary REF .
To extend the result of Corollary REF  to nonzero
\(\mathbf {M}_1\)  and \(\mathbf {M}_2\) , we will consider an enhancement argument, which
was first introduced by Weingarten, Steinberg and Shamai in
[1]}.
